library("scatterplot3d")
library('plotly')

Loading required package: ggplot2
Registered S3 methods overwritten by 'ggplot2':
  method         from 
  [.quosures     rlang
  c.quosures     rlang
  print.quosures rlang

Attaching package: 'plotly'

The following object is masked from 'package:ggplot2':

    last_plot

The following object is masked from 'package:stats':

    filter

The following object is masked from 'package:graphics':

    layout

path <- '../data/Oxygen.csv'
df <- read.csv(path, fileEncoding="UTF-8-BOM")

head(df)

Gender	x1	x2	x3	x4
1	0.34	3.71	2.87	30.87
1	0.39	5.08	3.38	43.85
1	0.48	5.13	4.13	44.51
1	0.31	3.95	3.60	46.00
1	0.36	5.51	3.11	47.02
1	0.33	4.07	3.95	48.50

Q1(a)

pairs(df[,-1])

x1 and x2, x3 and x4 have strong relationship

hist(df$x1)
hist(df$x2)
hist(df$x3)

Q1(b)

pairs(df[,-1], col=c('red', 'blue')[unclass(as.factor(df$Gender))])

male <- which(df$Gender == '1')
female <- which(df$Gender == '2')

pairs(df[male,-1])

pairs(df[female,-1])

hist(df[male, 2], col=rgb(1,0,0,0.3), border=rgb(0,0,0,0))
hist(df[female, 2], col=rgb(0,0,1,0.3), border=rgb(0,0,0,0), add=T)

hist(df[male, 3], col=rgb(1,0,0,0.3), border=rgb(0,0,0,0))
hist(df[female, 3], col=rgb(0,0,1,0.3), border=rgb(0,0,0,0), add=T)

hist(df[male, 4], col=rgb(1,0,0,0.3), border=rgb(0,0,0,0))
hist(df[female, 4], col=rgb(0,0,1,0.3), border=rgb(0,0,0,0), add=T)

scatterplot3d(df[,c(2,3,4)], pch=16, color="steelblue")
scatterplot3d(df[,c(2,3,5)], pch=16, color="steelblue")
scatterplot3d(df[,c(3,4,5)], pch=16, color="steelblue")

fig <- plot_ly(df, x=~x1, y=~x2, z=~x3, color=~Gender, colors=c('red','blue'))
fig <- fig %>% layout(scene = list(xaxis = list(title = 'x1'),
                     yaxis = list(title = 'x2'),
                     zaxis = list(title = 'x3')))
fig

No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode
No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode

fig <- plot_ly(df, x=~x1, y=~x2, z=~x4, color=~Gender, colors=c('red','blue'))
fig <- fig %>% layout(scene = list(xaxis = list(title = 'x1'),
                     yaxis = list(title = 'x2'),
                     zaxis = list(title = 'x3')))

fig

No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode
No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode

fig <- plot_ly(df, x=~x2, y=~x3, z=~x4, color=~Gender, colors=c('red','blue'))
fig <- fig %>% layout(scene = list(xaxis = list(title = 'x1'),
                     yaxis = list(title = 'x2'),
                     zaxis = list(title = 'x3')))

fig

No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode
No trace type specified:
  Based on info supplied, a 'scatter3d' trace seems appropriate.
  Read more about this trace type -> https://plot.ly/r/reference/#scatter3d
No scatter3d mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode

qqnorm(df$x1)
qqline(df$x1)
qqnorm(df$x2)
qqline(df$x2)
qqnorm(df$x3)
qqline(df$x3)
qqnorm(df$x4)
qqline(df$x4)

qqnorm(df[male, 2])
qqline(df[male, 2])
qqnorm(df[male, 3])
qqline(df[male, 3])
qqnorm(df[male, 4])
qqline(df[male, 4])
qqnorm(df[male, 5])
qqline(df[male, 5])

qqnorm(df[female, 2])
qqline(df[female, 2])
qqnorm(df[female, 3])
qqline(df[female, 3])
qqnorm(df[female, 4])
qqline(df[female, 4])
qqnorm(df[female, 5])
qqline(df[female, 5])

shapiro.test(df$x1)
shapiro.test(df$x2)
shapiro.test(df$x3)
shapiro.test(df$x4)

	Shapiro-Wilk normality test

data:  df$x1
W = 0.96894, p-value = 0.2094

	Shapiro-Wilk normality test

data:  df$x2
W = 0.90363, p-value = 0.0006346

	Shapiro-Wilk normality test

data:  df$x3
W = 0.94611, p-value = 0.02368

	Shapiro-Wilk normality test

data:  df$x4
W = 0.97328, p-value = 0.3131

shapiro.test(df[male, 2])
shapiro.test(df[male, 3])
shapiro.test(df[male, 4])
shapiro.test(df[male, 5])

	Shapiro-Wilk normality test

data:  df[male, 2]
W = 0.96123, p-value = 0.4396

	Shapiro-Wilk normality test

data:  df[male, 3]
W = 0.96721, p-value = 0.5753

	Shapiro-Wilk normality test

data:  df[male, 4]
W = 0.93163, p-value = 0.09478

	Shapiro-Wilk normality test

data:  df[male, 5]
W = 0.93961, p-value = 0.145

shapiro.test(df[female, 2])
shapiro.test(df[female, 3])
shapiro.test(df[female, 4])
shapiro.test(df[female, 5])

	Shapiro-Wilk normality test

data:  df[female, 2]
W = 0.85519, p-value = 0.002213

	Shapiro-Wilk normality test

data:  df[female, 3]
W = 0.84752, p-value = 0.001581

	Shapiro-Wilk normality test

data:  df[female, 4]
W = 0.96358, p-value = 0.4902

	Shapiro-Wilk normality test

data:  df[female, 5]
W = 0.94409, p-value = 0.1839